The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X X^2  1 X^2  1
 0 X^3+X^2  0  0  0 X^2 X^3+X^2 X^2  0  0  0  0 X^2 X^3+X^2 X^2 X^3+X^2  0 X^3 X^2 X^3+X^2 X^3  0 X^3+X^2 X^2  0 X^3 X^3+X^2 X^3+X^2 X^3  0 X^2 X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^3+X^2  0  0 X^2 X^3 X^3 X^2 X^3+X^2  0 X^3+X^2 X^2  0  0 X^3 X^3 X^3+X^2 X^3+X^2 X^3 X^2  0 X^2 X^2 X^2 X^3 X^3 X^3+X^2  0 X^3+X^2 X^3 X^2 X^3 X^3+X^2 X^3  0 X^3+X^2 X^3+X^2  0 X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^2  0 X^3+X^2
 0  0 X^3+X^2  0 X^2 X^2 X^3+X^2  0 X^2  0  0 X^3+X^2 X^2 X^3+X^2  0  0  0 X^3+X^2 X^3+X^2 X^3  0 X^3+X^2 X^3+X^2 X^3 X^3  0 X^3+X^2 X^2 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^3  0  0 X^3 X^2 X^2 X^3+X^2  0 X^2 X^2 X^3 X^2  0 X^3+X^2 X^3 X^3+X^2 X^3 X^2  0 X^3  0 X^3 X^3 X^2 X^2  0 X^2 X^3 X^2 X^2 X^3+X^2 X^3+X^2  0 X^2 X^2 X^3+X^2 X^2 X^2 X^3 X^3 X^3 X^3+X^2 X^2 X^2  0 X^3 X^2 X^3
 0  0  0 X^3+X^2 X^2  0 X^3+X^2 X^2 X^2  0 X^3+X^2  0  0 X^3+X^2 X^2  0 X^3 X^2 X^2  0 X^2 X^3  0 X^2 X^3 X^3+X^2 X^3 X^2  0 X^3+X^2 X^2 X^3  0 X^2 X^3 X^2 X^3 X^3+X^2  0 X^3+X^2  0 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^3  0 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^3  0 X^3+X^2  0 X^2 X^3 X^3  0 X^3+X^2 X^3  0 X^2 X^2 X^3+X^2 X^3 X^3  0 X^3  0 X^3+X^2 X^3  0 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^3 X^2 X^3
 0  0  0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3  0  0 X^3  0 X^3  0 X^3 X^3  0  0  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3 X^3  0  0 X^3 X^3  0  0  0 X^3  0  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0 X^3

generates a code of length 81 over Z2[X]/(X^4) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+167x^76+160x^79+369x^80+704x^81+256x^82+160x^83+166x^84+62x^88+2x^92+1x^156

The gray image is a linear code over GF(2) with n=648, k=11 and d=304.
This code was found by Heurico 1.16 in 1.88 seconds.